On automorphisms of algebraic K3 surfaces which act trivially on Picard groups (Q580465)

Let X be a complex algebraic K3 surface. As it is known \(H^ 2(X,{\mathbb{Z}})\) is a rank 22 lattice. Denote by \(S_ X\) the Picard group of X and consider the orthogonal complement \(T_ X\) of \(S_ X\) in \(H^ 2(X,{\mathbb{Z}})\). - The author studies automorphisms of X which act trivially on \(S_ X\), i.e. the group \(H_ X=\ker (Aut(X)\to Aut(S_ X))\). In particular if \(T_ X\) is unimodular he shows that the order of \(H_ X\), \(m_ X\), is a divisor of 66, 42 or 12. Moreover explicit examples of algebraic K3 surfaces with \(m_ X=66, 42\) are constructed.